MEI Conference 2015
IQR:Probability and
risk
Katharine Davies
katharine.davies@mei.org.uk
MEI Introduction to Quantitative Methods
Risk
Section 3: Risk
Worksheet: Probability and impact
Put the following events in the correct boxes.
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


An airplane crash
Shake hands with someone who has a cold and get a cold
Smoking 50 cigarettes a day and having health problems.
Rain stopping the Wimbledon’s men’s final.
Probability of the event
Can you fill in other events in each box?
Medium risk
High risk
Low risk
Medium risk
Impact of the event
Produced by MEI on behalf of OCR
© OCR 2014
Page 1
Probability format
The probability a woman at age 50 who participates in a routine
screening actually has breast cancer 0.01 (1%).
If a woman has breast cancer, the probability she will get a positive test
result in a routine screening is 0.80 (80%).
If a woman does not have breast cancer, the probability she will also get
a positive test result in a routine screening is 0.096 (9.6%).
A woman in this age group has a positive test result for breast cancer in
a routine screening. What is the probability she genuinely has breast
cancer?
Frequency format
10 of every 1000 women aged 50 who participate in routine screening
actually have breast cancer.
8 of every 10 women with breast cancer will get a positive test result in a
routine screening.
95 of 990 women who do not have breast cancer will also get a positive
test result in a routine screening.
In a representative sample of women aged 50 who got a positive result
in a routine screening, how many will you expect to genuinely have
breast cancer? Express your answer as number out of number.
Now express your answer as a probability.
Pictorial format
The diagram below presents frequencies for a representative sample of
1000 women aged 50 who are given a routine screening for breast
cancer.
Cancer and No Cancer refer to the presence or absence of the disease.
Positive and Negative refer to positive and negative test results during
routine screening.
In a representative sample of women aged 50 who got a positive result
in a routine screening, how many will you expect to genuinely have
breast cancer? Express your answer as number out of number.
Now express your answer as either a probability or as a percentage.
NOTE: One of the numbers in the diagram above is wrong – you need to
find and correct it before completing the task.
Traffic lights
On his way home from work each evening Sam has to pass through three sets of traffic lights in
the city centre.
The probabilities that he can pass through them without having to stop are 0.3, 0.2 and 0.5
respectively.
a)
b)
c)
Draw a tree diagram to represent this information
Find the probability that Sam does not have to stop at any of the three sets of lights
Find the probability that Sam has to stop at two or more sets of traffic lights.